Chiral N-Heterocyclic Carbene Catalyzed Annulations of Enals and Ynals with Stable Enols: A Highly Enantioselective Coates-Claisen Rearrangement

A combination of a chiral N-heterocyclic carbene catalyst and α,β-unsaturated aldehyde leads to a catalytically generated α,β-unsaturated acyl azolium, which participates in a highly enantioselective annulation to give dihydropyranone products. This full account of our investigations into the scope and mechanism of this reaction reveals the critical role of both the type and substitution pattern of the chiral triazolium precatalyst in inducing and controlling the stereochemistry. In an effort to explain why stable enols such as naphthol, kojic acid, and dicarbonyl are uniquely efficient, we have postulated that this annulation occurs via a Coates-Claisen rearrangement that invokes the formation of a hemiacetal prior to a sigmatropic rearrangement. Detailed kinetic investigations of the catalytic annulation are consistent with this mechanistic postulate.     

Positive solutions for fractional differential systems with nonlocal Riemann–Liouville fractional integral boundary conditions

In this paper, we study the positive solutions of fractional differential system with coupled nonlocal Riemann–Liouville fractional integral boundary conditions. Our analysis relies on Leggett–Williams and Guo–Krasnoselskii’s fixed point theorems. Two examples are worked out to illustrate our main results.     

Boundary Value Problems for Riemann–Liouville Fractional Differential Inclusions with Nonlocal Hadamard Fractional Integral Conditions

In this paper, we study a new class of boundary value problems from a fractional differential inclusion of Riemann–Liouville type and nonlocal Hadamard fractional integral boundary conditions. Some new existence results for convex as well as non-convex multi-valued maps are obtained using standard fixed point theorems. The obtained results are illustrated by examples.     

Catalytic Selective Synthesis

Complete control of the product of a catalytic reaction can be achieved on the basis of catalyst structure, even when the reaction conditions are nearly identical. Catalyst‐controlled selectivity is well established for enantioselective catalysis but less formulated for catalytic regio‐, chemo‐, or product‐selective reactions. This Review describes selective transformations of the same starting materials into two or more different products simply by the choice of catalyst. By collecting and highlighting examples of selective catalysis, we hope that the field will be encouraged by the progress that has been made while bringing attention to unmet needs in the design and mechanistic understanding of selective catalysts.     

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.     

Boundary value problems for first order functional differential equations with impulsive integral conditions

In this paper, by using the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition. Some comparison results are also formulated.     

Fractional Differential Equations with Nonlocal Integral and Integer–Fractional-Order Neumann Type Boundary Conditions

We introduce a new concept of the coupling of nonlocal integral and integer–fractional-order Neumann type boundary conditions, and discuss the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with these conditions. The existence of solutions is derived from Leray–Schauder’s alternative and Schauder’s fixed point theorem, while the uniqueness of solutions is established by means of Banach’s contraction mapping principle. The results obtained in this paper are well illustrated with the aid of examples.